3. Functions

Determine whether each function graphed or defined is one-to-one. y = x+4 / x-3

Use the graphs of f and g to solve Exercises 83–90.

Find the domain of ƒ/g.

In Exercises 101–102, find an equation for f^(-1)(x). Then graph f and f^(-1) in the same rectangular coordinate system. f(x) = 1 - x^2, x ≥ 0.

Given functions f and g, find (b)(g∘ƒ)(x) and its domain. See Examples 6 and 7.

$\text{ƒ}\left(x\right)=\frac{2}{x},g\left(x\right)=x+1$

Let ƒ(x)=x²+3 and g(x)=-2x+6. Find each of the following. (ƒ+g)(3)

Let ƒ(x)=2x-3 and g(x)=-x+3. Find each function value. See Example 5.

$(\text{ƒ}\circ g)\left(4\right)$

Find fg and determine the domain for each function. f(x) = 3 − x², g(x) = x² + 2x − 15

Find f(g(x)) and g (f(x)) and determine whether each pair of functions ƒ and g are inverses of each other. f(x)=5x-9 and g(x) = (x+5)/9

The functions in Exercises 93–95 are all one-to-one. For each function, (a) find an equation for f^(-1)x, the inverse function. (b) Verify that your equation is correct by showing that f(f^(-1)(x)) = x and f^(-1)(f(x)) = x. f(x) = (x - 7)/(x + 2)

For the pair of functions defined, find (ƒg)(x).Give the domain of each. See Example 2.

ƒ(x)=3x+4, g(x)=2x-7

Find f−g and determine the domain for each function. f(x) = 2x² − x − 3, g (x) = x + 1

Express the given function h as a composition of two functions ƒ and g so that h(x) = (fog) (x).

h(x) = 1/(2x-3)

Given functions f and g, find (a)(ƒ∘g)(x) and its domain, and (b)(g∘ƒ)(x) and its domain. See Examples 6 and 7.

$\text{ƒ}\left(x\right)=\surd (x+4),g\left(x\right)=-\left(\frac{2}{x}\right)$

For the pair of functions defined, find (ƒ-g)(x).Give the domain of each. See Example 2.

ƒ(x)=√(4x-1), g(x)=1/x

Use a graphing calculator to graph each equation in the standard viewing window. y = 3x + 4